# Complex-city

Algebra Level 4

Let the number of all complex numbers $$z_1$$ which satisfy $$z_1^{3}-\bar{z_1}=0$$ be $$a$$.

If $$\arg\left(\dfrac{z_2-2}{z_2+2}\right)=\dfrac{\pi}{4}$$, then locus of $$z_2$$ is $$|z_2-bi|=\sqrt{c}$$.

Find $$a+b+c$$.

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